Problem: $K$ is the midpoint of $\overline{JL}$ $J$ $K$ $L$ If: $ JK = 9x - 5$ and $ KL = 7x + 3$ Find $JL$.
Answer: A midpoint divides a segment into two segments with equal lengths. ${JK} = {KL}$ Substitute in the expressions that were given for each length: $ {9x - 5} = {7x + 3}$ Solve for $x$ $ 2x = 8$ $ x = 4$ Substitute $4$ for $x$ in the expressions that were given for $JK$ and $KL$ $ JK = 9({4}) - 5$ $ KL = 7({4}) + 3$ $ JK = 36 - 5$ $ KL = 28 + 3$ $ JK = 31$ $ KL = 31$ To find the length $JL$ , add the lengths ${JK}$ and ${KL}$ $ JL = {JK} + {KL}$ $ JL = {31} + {31}$ $ JL = 62$